Executive Summary

The authors are motivated by the problem of designing a simple distributed algorithm for peer-to-peer streaming applications that can achieve high throughput and low delay, while allowing the neighbor set maintained by each peer to be small. While previous works have mostly used tree structures, their algorithm constructs multiple random directed Hamiltonian cycles and disseminates content over the superposed graph of the cycles. The key theoretical contribution is to characterize the distance between peers in a graph formed by the superposition of directed random Hamiltonian cycles, in which edges from one of the cycles may be dropped at random. They use Doob martingales and graph expansion ideas to characterize this distance as a function of N, with high probability.